{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T22:03:27Z","timestamp":1761948207110,"version":"3.37.3"},"reference-count":32,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2023,2,17]],"date-time":"2023-02-17T00:00:00Z","timestamp":1676592000000},"content-version":"vor","delay-in-days":2359,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["IIS-1421780"],"award-info":[{"award-number":["IIS-1421780"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2017,6,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>In many applications involving point pattern data, the Poisson process assumption is unrealistic, with the data exhibiting a more regular spread. Such repulsion between events is exhibited by trees for example, because of competition for light and nutrients. Other examples include the locations of biological cells and cities, and the times of neuronal spikes. Given the many applications of repulsive point processes, there is a surprisingly limited literature developing flexible, realistic and interpretable models, as well as efficient inferential methods. We address this gap by developing a modelling framework around the Mat\u00e9rn type III repulsive process. We consider some extensions of the original Mat\u00e9rn type III process for both the homogeneous and the inhomogeneous cases. We also derive the probability density of this generalized Mat\u00e9rn process, allowing us to characterize the conditional distribution of the various latent variables, and leading to a novel and efficient Markov chain Monte Carlo algorithm. We apply our ideas to data sets of spatial locations of trees, nerve fibre cells and Greyhound bus stations.<\/jats:p>","DOI":"10.1111\/rssb.12198","type":"journal-article","created":{"date-parts":[[2016,9,2]],"date-time":"2016-09-02T12:34:25Z","timestamp":1472819665000},"page":"877-897","source":"Crossref","is-referenced-by-count":4,"title":["Bayesian Inference for Mat\u00e9rn Repulsive Processes"],"prefix":"10.1093","volume":"79","author":[{"given":"Vinayak","family":"Rao","sequence":"first","affiliation":[{"name":"Purdue University , West Lafayette , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ryan P.","family":"Adams","sequence":"additional","affiliation":[{"name":"Harvard University , Boston"},{"name":"Twitter , Boston , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"David D.","family":"Dunson","sequence":"additional","affiliation":[{"name":"Duke University , Durham , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2016,9,2]]},"reference":[{"volume-title":"Kernel methods for nonparametric Bayesian inference of probability densities and point processes","year":"2009","author":"Adams","key":"2023021801100759500_rssb12198-cit-0001"},{"key":"2023021801100759500_rssb12198-cit-0002","first-page":"9","volume-title":"Tractable nonparametric Bayesian inference in Poisson processes with Gaussian process intensities","author":"Adams","year":"2009"},{"key":"2023021801100759500_rssb12198-cit-0003","first-page":"1224","volume-title":"Learning the parameters of determinantal point process kernels","author":"Affandi","year":"2014"},{"key":"2023021801100759500_rssb12198-cit-0004","doi-asserted-by":"crossref","first-page":"697","DOI":"10.1214\/07-AOS574","article-title":"The pseudo-marginal approach for efficient Monte Carlo computations","volume":"37","author":"Andrieu","year":"2009","journal-title":"Ann. Statist."},{"key":"2023021801100759500_rssb12198-cit-0005","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1111\/1467-9574.00144","article-title":"Non- and semi-parametric estimation of interaction in inhomogeneous point patterns","volume":"54","author":"Baddeley","year":"2000","journal-title":"Statist. Neerland."},{"key":"2023021801100759500_rssb12198-cit-0006","first-page":"1","article-title":"Spatstat: an R package for analyzing spatial point patterns","volume":"12","author":"Baddeley","year":"2005","journal-title":"J. Statist. Softwr."},{"key":"2023021801100759500_rssb12198-cit-0007","first-page":"193","article-title":"Discussion on \u2018Modelling spatial patterns\u2019 (by B. D. Ripley)","volume":"39","author":"Besag","year":"1977","journal-title":"J. R. Statist. Soc. B"},{"key":"2023021801100759500_rssb12198-cit-0008","first-page":"253","volume-title":"Computational Neuroscience: a Comprehensive Approach","author":"Brown","year":"2004"},{"key":"2023021801100759500_rssb12198-cit-0009","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-49835-5","volume-title":"An Introduction to the Theory of Point Processes","author":"Daley","year":"2008"},{"key":"2023021801100759500_rssb12198-cit-0010","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198510550.001.0001","volume-title":"Highly Structured Stochastic Systems","author":"Green","year":"2003"},{"key":"2023021801100759500_rssb12198-cit-0011","doi-asserted-by":"crossref","first-page":"225","DOI":"10.2307\/2258930","article-title":"The intensity of spatial pattern in plant communities","volume":"61","author":"Hill","year":"1973","journal-title":"J. Ecol."},{"key":"2023021801100759500_rssb12198-cit-0012","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1214\/154957806000000078","article-title":"Determinantal processes and independence","volume":"3","author":"Hough","year":"2006","journal-title":"Probab. Surv."},{"key":"2023021801100759500_rssb12198-cit-0013","doi-asserted-by":"crossref","first-page":"958","DOI":"10.1239\/aap\/1261669580","article-title":"Likelihood-based inference for Mat\u00e9rn type III repulsive point processes","volume":"41","author":"Huber","year":"2009","journal-title":"Adv. Appl. Probab."},{"key":"2023021801100759500_rssb12198-cit-0014","doi-asserted-by":"crossref","first-page":"21","DOI":"10.2307\/2980138","article-title":"The geographical distribution of crop productivity in England (with discussion)","volume":"102","author":"Kendall","year":"1939","journal-title":"J. R. Statist. Soc."},{"key":"2023021801100759500_rssb12198-cit-0015","first-page":"384","volume-title":"The Challenge of Epidemiology: Issues and Selected Readings","author":"Knox","year":"2004"},{"key":"2023021801100759500_rssb12198-cit-0016","doi-asserted-by":"crossref","first-page":"1026","DOI":"10.1287\/opre.27.5.1026","article-title":"Simulation of nonhomogeneous Poisson processes with degree-two exponential polynomial rate function","volume":"27","author":"Lewis","year":"1979","journal-title":"Ops Res."},{"key":"2023021801100759500_rssb12198-cit-0017","doi-asserted-by":"crossref","first-page":"344","DOI":"10.1111\/j.1467-9574.1996.tb01501.x","article-title":"A nonparametric measure of spatial interaction in point patterns","volume":"50","author":"van Lieshout","year":"1996","journal-title":"Statist. Neerland."},{"key":"2023021801100759500_rssb12198-cit-0018","article-title":"Spatial variation","volume":"49","author":"Mat\u00e9rn","year":"1960","journal-title":"Medd. Statns Skogsforskinst."},{"key":"2023021801100759500_rssb12198-cit-0019","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4615-7892-5","volume-title":"Spatial Variation","author":"Mat\u00e9rn","year":"1986"},{"key":"2023021801100759500_rssb12198-cit-0020","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1111\/j.1751-5823.2001.tb00481.x","article-title":"Likelihood inference for Gibbs processes in the analysis of spatial point patterns","volume":"69","author":"Mateu","year":"2001","journal-title":"Int. Statist. Rev."},{"key":"2023021801100759500_rssb12198-cit-0021","doi-asserted-by":"crossref","first-page":"2142","DOI":"10.1016\/j.spa.2010.06.002","article-title":"Perfect simulation and moment properties for the Mat\u00e9rn type-III process","volume":"120","author":"M\u00f8ller","year":"2010","journal-title":"Stoch. Processes Appl."},{"key":"2023021801100759500_rssb12198-cit-0022","doi-asserted-by":"crossref","first-page":"643","DOI":"10.1111\/j.1467-9469.2007.00569.x","article-title":"Modern statistics for spatial point processes","volume":"34","author":"M\u00f8ller","year":"2007","journal-title":"Scand. J. Statist."},{"key":"2023021801100759500_rssb12198-cit-0023","first-page":"1723","volume-title":"Advances in Neural Information Processing Systems","author":"Murray","year":"2010"},{"key":"2023021801100759500_rssb12198-cit-0024","first-page":"541","volume-title":"Elliptical slice sampling","author":"Murray","year":"2010"},{"key":"2023021801100759500_rssb12198-cit-0025","first-page":"197","article-title":"The nature of the distribution of galaxies","volume":"32","author":"Peebles","year":"1974","journal-title":"Astron. Astrophys."},{"key":"2023021801100759500_rssb12198-cit-0026","first-page":"7","article-title":"CODA: convergence diagnosis and output analysis for MCMC","volume":"6","author":"Plummer","year":"2006","journal-title":"R News"},{"key":"2023021801100759500_rssb12198-cit-0027","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511624131","volume-title":"Statistical Inference for Spatial Processes","author":"Ripley","year":"1988"},{"key":"2023021801100759500_rssb12198-cit-0028","doi-asserted-by":"crossref","first-page":"2310","DOI":"10.1016\/j.cor.2005.09.005","article-title":"A review of hierarchical facility location models","volume":"34","author":"\u015eahin","year":"2007","journal-title":"Comput. Ops Res."},{"key":"2023021801100759500_rssb12198-cit-0029","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevE.79.041108","article-title":"Statistical properties of determinantal point processes in high-dimensional Euclidean spaces","volume":"79","author":"Scardicchio","year":"2009","journal-title":"Phys. Rev. E"},{"key":"2023021801100759500_rssb12198-cit-0030","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-4250-5","volume-title":"Theory of Statistics","author":"Schervish","year":"1995"},{"key":"2023021801100759500_rssb12198-cit-0031","first-page":"207","volume-title":"Proc. 3rd Conf. Advisory Group of Forest Statisticians","author":"Strand","year":"1972"},{"key":"2023021801100759500_rssb12198-cit-0032","doi-asserted-by":"crossref","first-page":"2827","DOI":"10.1002\/sim.4315","article-title":"Second-order spatial analysis of epidermal nerve fibers","volume":"30","author":"Waller","year":"2011","journal-title":"Statist. Med."}],"container-title":["Journal of the Royal Statistical Society Series B: Statistical Methodology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2Frssb.12198","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2Frssb.12198","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1111\/rssb.12198","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1111\/rssb.12198","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/am-pdf\/10.1111\/rssb.12198","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/79\/3\/877\/49215185\/jrsssb_79_3_877.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/79\/3\/877\/49215185\/jrsssb_79_3_877.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,19]],"date-time":"2024-06-19T05:05:45Z","timestamp":1718773545000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/79\/3\/877\/7040709"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,9,2]]},"references-count":32,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2016,9,2]]},"published-print":{"date-parts":[[2017,6,1]]}},"URL":"https:\/\/doi.org\/10.1111\/rssb.12198","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"type":"print","value":"1369-7412"},{"type":"electronic","value":"1467-9868"}],"subject":[],"published-other":{"date-parts":[[2017,6]]},"published":{"date-parts":[[2016,9,2]]}}}